How do you express $x^3/[x(x^2+2x+1)]$ in partial fractions?

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Answer 1 · 2016-04-13T05:42:01

$x^3/(x(x^2+2x+1))=1-2/(x+1)+1/(x+1)^2$

This one is relatively simpler and need for detailed solution as given here, does not arise.

$x^3/(x(x^2+2x+1))=x^2/(x^2+2x+1)=(x^2+2x+1-(2x+1))/(x^2+2x+1)$

= $1-(2x+1)/(x+1)^2$

= $1-(2x+2-1)/(x+1)^2$

= $1-(2(x+1))/(x+1)^2+1/(x+1)^2$ or

= $1-2/(x+1)+1/(x+1)^2$

How do you express x^3/[x(x^2+2x+1)]x^3/[x(x^2+2x+1)] in partial fractions?